The photorefractive effect is an interesting physical phenomenon with substantial technological importance. Its potential for optical processing and optical computing applications has been demonstrated in crystals, such as bismuth silicon oxide (Bi.sub.12 SiO.sub.20), barium titanate (BaTiO.sub.3), lithium niobate (LiNbO.sub.3) and strontium barium niobate (Sr.sub.0.6 Ba.sub.0.4 Nb.sub.2 O.sub.6).
However, these oxide materials have two major weak points towards actual applications. These weaknesses include:(1) their photorefractive response is too slow, and(2) their operation wavelength is in the range of 0.4 to 0.7 .mu.m, requiring gas lasers which are expensive, fragile, and large in size. These weaknesses limit the applications of these materials. For example, these oxide materials are not desirable for applications requiring high-speed, real-time operation with low-power consumption in a compact system.
Matrix-vector multiplication is a basic operation in matrix algebra with a variety of applications, especially in signal and image processing, optical interconnects, and neural networks. Because of the high degree of parallelism in optics, optical techniques can offer a great advantage in speed by performing operations concurrently. A considerable amount of work has been reported on performing matrix-vector multiplication using conventional optical means. Recently, Yeh and Chiou described a method of using four-wave mixing in nonlinear media to perform matrix-vector multiplication; see, Opt. Lett., Vol. 12, pp. 138-140 (1987); Technical Digest of the 1986 Annual Meeting of the Optical Society of America, Seattle, WA. The authors demonstrated the concept using a photorefractive BaTiO.sub.3 crystal. The possibility of performing the summation in a four-wave mixing process was pointed out by Yeh and Chiou.
However, the aforementioned weaknesses limit the use of photorefractive oxides, such as BaTiO.sub.3, in matrix multiplication. In addition, these oxides cannot be integrated together with the existing electronic and optoelectronic technologies.
Optical information systems are built with conventional discrete active processors and passive components. These systems are physically large, limiting applications. Currently, integrated optics concerns mainly the integration of optoelectronics and electronics using the planar technology. This also restricts the utilization of the full potential of optics.
It is desired to provide optical processing in materials that enjoy compatibility with existing electronic and optoelectronic systems. Such materials should be faster than the photorefractive oxides and be capable of operating in regions accessible to semiconductor lasers.